E4004 Surveying Computations A Area Problems

To Cut Off an Area by a Line Passing Through a Fixed Point The bearing and distance BP is known B P X Brg Dist Brg The bearing BX is known The required area BPX is known Calculate the bearing and distance PX and the distance BX

To Cut Off an Area by a Line Passing Through a Fixed Point The angle at B is determined from the bearing difference B P X Brg Dist Brg The general formula for the area of a triangle is C B A a b

To Cut Off an Area by a Line Passing Through a Fixed Point The bearing & distance of the line PX can be calculated by closing PBX B P X Brg Dist Brg Also check that the area PBX calculates to the correct area by using the CLOSE program

To Cut Off an Area by a Line Passing Through a Particular Point A farmer wants to fence off a particular area from a large paddock.There is an existing trough which must be accessible to stock on both sides of the new fence.

To Cut Off an Area by a Line Passing Through a Particular Point The bearings of BC and BD are known. B C D Brg The bearing and distance BP can be measured. Brg Dist P The required area is  A

To Cut Off an Area by a Line Passing Through a Particular Point Note that there will be two solutions B C D Brg Dist P Such that C’ D’

To Cut Off an Area by a Line Passing Through a Particular Point B C D Brg Dist P x y   Let

To Cut Off an Area by a Line Passing Through a Particular Point B C D Brg Dist P x y  

To Cut Off an Area by a Line Passing Through a Particular Point B C D Brg Dist P x y   Multiply both sides of the equation by, x sin(  ) Re-write in terms of x

To Cut Off an Area by a Line Passing Through a Particular Point B C D Brg Dist P x y   This equation is in quadratic form and can be solved for x Make the LHS equal zero

To Cut Off an Area by a Line Passing Through a Particular Point Write a program to solve for x in a quadratic given values for a, b and c OR write a solver program which will solve for x, a, b or c

To Cut Off an Area by a Line Passing Through a Particular Point When the Figure is not a Triangle It is required to cut off a given area CQRSTD by a line passing through P C Q R S T D P The bearings and distances QR, RS and ST are known whilst the position of P has been located from Q Brg & Dist Only the bearings are known for CQ and TD Brg AA

To Cut Off an Area by a Line Passing Through a Particular Point When the Figure is not a Triangle Extend CQ and DT to intersect at B C Q R S T D P The figure CBDF is the same as that formed in the earlier example provided the required area is made equal to the sum of Area QRSTB and  A Brg & Dist Brg B AA The dimensions of lines TB and BQ can be calculated by closing QRSTB and the line BP by closing BQP